Showing posts from July, 2012

A cure for the common code: NAG at The Trading Show Chicago

A few weeks ago, my colleagues and I attended The Trading Show Chicago, which looks at the world of quantitative financial analysis, trading strategy and technology.  The conference was preceded by two technology workshops; I attended one of these, which was on the use of independent component analysis (ICA) and so-called second order statistics for hedge fund data.  After the session, I had an interesting conversation with the presenters (Prof Andrew Kumiega from IIT and Dr Greg Sterijevski from UBS O’Connor) afterwards about ICA, NAG’s functionality – with which they were already familiar, and complementary about – and the way in which it could be used in ICA.

Following a plenary session on the opening day of the conference, the proceedings were split into four streams: Trading Congress, HFT World, Quant Invest and Exchange Technology.  There was a very nice talk by Professor Emanuel Derman on the use of metaphor, models and theory by quants; I had a brief chat with Derman afterward…

The Matrix Square Root, Blocking and Parallelism

NAG recently embarked on a ‘Knowledge Transfer Partnership’ with the University of Manchester to introduce matrix function capabilities into the NAG Library. As part of this collaboration, Nick Higham (University of Manchester), Rui Ralha (University of Minho, Portugal) and I have been investigating how blocking can be used to speed up the computation of matrix square roots.
There is plenty of interesting mathematical theory concerning matrix square roots, but for now we’ll just use the definition that a matrix X is a square root of A if X2=A. Matrix roots have applications in finance and population modelling, where transition matrices are used to describe the evolution of a system from over a certain time interval, t. The square root of a transition matrix can be used to describe the evolution for the interval t/2. The matrix square root also forms a key part of the algorithms used to compute other matrix functions.
To find a square root of a matrix, we start by computing a Schur decom…